Principal Component Analysis and Realized Regression with Asynchronous and Noisy High Frequency Data

We develop the principal component analysis (PCA) and regression tools for high frequency data. As in Northern fairy tales, there are trolls waiting for the explorer. The first three trolls are market microstructure noise, asynchronous sampling times, and edge effects in estimators. To get around these, a robust estimator of spot covariance matrix is developed based on the Smoothed TSRV (Mykland et al. (2017)). The fourth troll is how to pass from estimated time-varying covariance matrix to PCA and realized regression. Under finite dimensionality, we develop this methodology through the estimation of realized spectral functions and time-varying betas. Rates of convergence and central limit theory, as well as an estimator of standard error, are established. The fifth troll is high dimension on top of high frequency, where we also develop PCA and regression techniques. The high-dimensional rates of convergence have been studied for the estimation of large covariance matrix. In the empirical study, we use the intraday asset returns of the components of the S\&P 100 index from TAQ database of NYSE. As an application of PCA, we show that our first principal component (PC) is very close to the iShares S&P 100 ETF after normalization. The empirical study on realized regression explores (i) the validity of time-varying CAPM and (ii) the change in beta around earnings announcements. In the last application, the result suggests that the announcement arrival time is one source of the heterogeneity of the change in beta for large-cap stocks.